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Problem of the Week

Problem B and Solution

Squirrelly Over Nuts


Squiggles the Squirrel loves nuts. He has to be sure that he has enough for the winter, so he decides to hide a bunch around his yard. He buries them in a special way so that he will be able to find them. A portion of his yard is shown as a grid below.

In hiding the nuts, he uses the following plan. Starting at \(X\) he buries 2 nuts. He will then repeat the following three steps.

  1. He moves 2 m north, 3 m east, and 1 m south, and then buries 3 nuts.

  2. He moves 3 m north, 3 m east, and 2 m south, and then buries 5 nuts.

  3. He moves 4 m north, 3 m east, and 3 m south, and then buries 8 nuts.

EXTENSION: Examine the points on your grid from part b). Describe how Squiggles could reach his hiding spots with the least amount of running around.


EXTENSION: The grid below reveals that Squiggles’ nuts are buried at points along the straight line (dotted) which, in effect, follows the pattern for every one square north it goes three squares east. Since the shortest distance between two points is along a straight line, he could save a lot of time and energy by just moving along this line and hiding his nuts at the appropriate points.
(But he’s a squirrel, so he naturally likes to run about erratically!)

A line passing through X and the six other points.